Simplify the following expression and state the condition under which the simplification is valid. You can assume that $p \neq 0$. $t = \dfrac{-5}{7(4p + 7)} \div \dfrac{9}{8(4p + 7)} $
Dividing by an expression is the same as multiplying by its inverse. $t = \dfrac{-5}{7(4p + 7)} \times \dfrac{8(4p + 7)}{9} $ When multiplying fractions, we multiply the numerators and the denominators. $t = \dfrac{ -5 \times 8(4p + 7) } { 7(4p + 7) \times 9 } $ $ t = \dfrac{-40(4p + 7)}{63(4p + 7)} $ We can cancel the $4p + 7$ so long as $4p + 7 \neq 0$ Therefore $p \neq -\dfrac{7}{4}$ $t = \dfrac{-40 \cancel{(4p + 7})}{63 \cancel{(4p + 7)}} = -\dfrac{40}{63} $